How to Slow Down Faster: The Math behind Brakes. Part 3: Brake Bias

Part 1 is here.

Part 2 is here.

Part 2b is here.

     Now that we’re able to calculate the approximate brake force and stopping distance, let’s compare what we’ve learned to the real world.

     In the equations, we can figure out the brake force of one corner, the total brake force of the car, and its deceleration due to the brakes.  We’ve only so far used the car’s total weight with the total brake force, but we’re going to break that down even further.  The car’s front to rear weight ratio is important now that we’re going to divide the total brake force into the front and the rear.  A front:rear weight ratio basically tells us how much weight is on the front tires compared to the rear tires, and if we have the total gross weight, we can easily figure out how much weight is distributed between the front and back.  Why is this important?  Because so far, we’ve only been plugging in the car’s total weight, not putting into consideration the fact that car’s are never perfectly balanced 50/50 between front and rear and the fact that there’s weight transfer.

     Up to now, we considered the total car’s weight to be evenly distributed between the front and rear.  But now lets add in the fact that a car’s weight isn’t perfectly distributed between the front and rear.  What now?  We’ll break the car down into two parts; the front and the rear.  That way we can calculate the brake force and Decleration seperately.  Say we have a 3,000 pound vehicle with a 60/40 weight distribution.  We can then assume the front tires are propping up 1800 pounds, while the rear are holding up 1200 pounds.  So using our previous formulas, we just have to add two new equations:

     Instead of solving for the Total Brake Force and ending there, we keep on going to figure out the front or rear deceleration (please remember that the deceleration = the coefficient of friction.  refer back to part 1).  Remember that when you’re solving for either, that you plug in the right numbers for the rotor size, caliper piston area, etc. etc.  Now that we have different front:rear weights, and different front and rear brake sizes, you can imagine the Deceleration for the front will be different from the back.  That’s not what we want, because in real life, a car with a balanced brake system will always stop faster and earlier than a brake system that’s too front or rear biased.  Also, remember that all tires have a maximum amount of grip.  They cannot stop faster than they can grip, and since Deceleration = Mu, the car’s deceleration is how much the tires and grip.  Too front biased and you might exceed the front tire’s grip limits.  Too much to the rear and the same might happen.  If that does, your ABS will have to kick in, and prolong your brake time and distance.

     Now that we’ve factored in front:rear weight ratios, there’s one more variable we have to consider.  And that’s weight transfer.  That’s what happens when you brake, accelerate, or turn, and you feel like your being pulled/pushed in a different direction.  That’s for the next post.  Stay tuned.